It doesn't matter how much memory the graphics card has, your PC will support it.
The important thing when you choose a graphics card is in making sure your PC's motherboard has an expansion slot which matches the card specifications (eg if you choose a PCI-Express x16 card, make sure your motherboard has a free PCI-Express x16 slot).
All gaming cards need a PCI-Express x16 slot, and the ASRock H81 PRO BTC motherboard has one of those slots so you are okay,
One other important consideration is in making sure the PSU is suitable for the graphics card you have chosen.
When you've chosen a graphics card, start a new thread and ask about the PSU you will need for it, remembering to include the make & model of your existing PSU.